/**********************************************************************
* Supplementary File: Complete Stata Output Log
* Study Title: THE RELATIONSHIP BETWEEN ACCOUNTING INFORMATION QUALITY AND MARKET VALUE IN BRAZILIAN COMPANIES
* Authors: Leite, J. P. P. C., Novais, F. M. O., Rossetti, N. & Carvalho, F. L..
* Date of Analysis: [2025-08-05]
*
* Description:
* This file contains the full output from the panel data analyses performed using Stata. The analyses include:
* - Panel structure definition
* - Descriptive statistics and outlier treatment via winsorization
* - Correlation matrices (raw and winsorized data)
* - Multiple regression models: OLS, Between Effects (BE), Fixed Effects (FE), Random Effects (RE)
* - Robustness checks including clustered robust standard errors
* - Diagnostic tests including Hausman test, Breusch-Pagan LM test, Modified Wald test for heteroskedasticity, and F-test for fixed effects
* - Models with year fixed effects to control for time-specific shocks
* - Additional models using alternative accounting quality proxies
*
* Notes:
* - All standard errors are robust and clustered by firm (Firm_id) where indicated.
* - Models are estimated on an unbalanced panel dataset covering years 2011-2020.
* - Please refer to the main manuscript for interpretation and discussion of the results.
*
* Software:
* Stata 15.0
**********************************************************************/


************************************************************************************************************************************************************************
** 1. Definition of the Panel Data Structure
** The database was organized for unbalanced panel analysis, identifying the cross-sectional units (Firm_id) and time periods (Year):

. xtset Firm_id Year
       panel variable:  Firm_id (unbalanced)
        time variable:  Year, 2011 to 2020, but with gaps
                delta:  1 year

************************************************************************************************************************************************************************
** 2. Descriptive Statistics, Treatment of Outliers, and Correlation Matrix

** 2.1 Descriptive Statistics

. sum MB DY Capex Size ROE Indebt Growth MdfjonesTACC

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          MB |      2,246    1.287663    .9295134     .03063    8.74298
          DY |      2,246    .0254954    .0515487          0     1.1143
       Capex |      2,246    .0641772    .1145064  -1.410909   .8668148
        Size |      2,246    6.483907    .7622121    3.07793     8.9945
         ROE |      2,246    .0428355    1.380666  -54.51531    17.9096
-------------+---------------------------------------------------------
      Indebt |      2,246    .5618502    .1892721     .03063     .99589
      Growth |      2,246    .1370166    .4244456    -.96736    7.35631
MdfjonesTACC |      2,246   -.0940384    2.602061  -102.7332   1.818373

** ==> Some outliers were observed. An analysis of the outliers was conducted to check if they were affecting the model.

** 2.2 Treatment of Outliers with Winsorization

ssc install winsor, replace

winsor MB, gen(MB_w) h(1)
winsor DY, gen(DY_w) h(1)
winsor Capex, gen(Capex_w) h(1)
winsor Size, gen(Size_w) h(1)
winsor ROE, gen(ROE_w) h(1)
winsor Indebt, gen(Indebt_w) h(1)
winsor Growth, gen(Growth_w) h(1)
winsor MdfjonesTACC, gen(MdfjonesTACC_w) h(1)

** ==> The winsorization technique was applied to limit extreme values within the interval between the 1st and 99th percentiles, minimizing the influence of outliers:

** 2.3 Descriptive Statistics for Winsorized Data

.  sum MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
        MB_w |      2,246    1.287501    .9282238     .03695    8.37421
        DY_w |      2,246    .0253615    .0490503          0     .81371
     Capex_w |      2,246    .0641888    .1142145   -1.36834   .8503816
      Size_w |      2,246    6.483995    .7617374    3.30336    8.96662
       ROE_w |      2,246    .0508325    .8022104  -21.27608    2.63168
-------------+---------------------------------------------------------
    Indebt_w |      2,246    .5618526    .1892633     .03695     .99494
    Growth_w |      2,246    .1361431    .4113923    -.96621     5.3933
MdfjonesTA~w |      2,246   -.0788119    2.033021  -68.03291   1.316795


** ==> The descriptive statistics indicate that winsorization has a limited impact on the mean values of most variables.


* 2.4 Comparative Correlation Matrix for Raw and Winsorized Variables

. correlate MB DY Capex Size ROE Indebt Growth MdfjonesTACC
(obs=2,246)

             |       MB       DY    Capex     Size      ROE   Indebt   Growth Mdfjon~C
-------------+------------------------------------------------------------------------
          MB |   1.0000
          DY |   0.0452   1.0000
       Capex |   0.0653  -0.0589   1.0000
        Size |   0.0679   0.0136   0.0512   1.0000
         ROE |   0.0458   0.0420   0.0382   0.0053   1.0000
      Indebt |  -0.0456  -0.1471   0.0920   0.2971  -0.0786   1.0000
      Growth |   0.0099  -0.0405   0.2724  -0.0038   0.0442   0.0346   1.0000
MdfjonesTACC |   0.0218   0.0123  -0.1909   0.0071   0.0035  -0.0182  -0.0379   1.0000

. correlate MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w
(obs=2,246)

             |     MB_w     DY_w  Capex_w   Size_w    ROE_w Indebt_w Growth_w Mdfjon~w
-------------+------------------------------------------------------------------------
        MB_w |   1.0000
        DY_w |   0.0490   1.0000
     Capex_w |   0.0656  -0.0605   1.0000
      Size_w |   0.0679   0.0181   0.0518   1.0000
       ROE_w |   0.0702   0.0706   0.0571   0.0241   1.0000
    Indebt_w |  -0.0457  -0.1490   0.0923   0.2973  -0.1122   1.0000
    Growth_w |   0.0120  -0.0428   0.2825   0.0003   0.0707   0.0362   1.0000
MdfjonesTA~w |   0.0224   0.0124  -0.1998   0.0059   0.0064  -0.0208  -0.0441   1.0000


** ==> The correlations among the variables after winsorization showed similar results.



** 2.5 Comparison of OLS with Raw and Winsorized Data:

** Raw Data: 

. reg MB DY Capex Size ROE Indebt Growth MdfjonesTACC

      Source |       SS           df       MS      Number of obs   =     2,246
-------------+----------------------------------   F(7, 2238)      =      5.77
       Model |  34.3619329         7  4.90884755   Prob > F        =    0.0000
    Residual |  1905.30726     2,238  .851343725   R-squared       =    0.0177
-------------+----------------------------------   Adj R-squared   =    0.0146
       Total |  1939.66919     2,245  .863995184   Root MSE        =    .92268

------------------------------------------------------------------------------
          MB |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          DY |   .6548535   .3833654     1.71   0.088    -.0969355    1.406642
       Capex |   .6205808   .1809463     3.43   0.001     .2657407    .9754209
        Size |   .1016229   .0268374     3.79   0.000     .0489941    .1542516
         ROE |   .0240656   .0141867     1.70   0.090    -.0037548     .051886
      Indebt |  -.3359606   .1097927    -3.06   0.002    -.5512667   -.1206545
      Growth |  -.0155345   .0477492    -0.33   0.745    -.1091718    .0781029
MdfjonesTACC |   .0120601   .0076266     1.58   0.114    -.0028959    .0270161
       _cons |    .763218   .1674246     4.56   0.000     .4348942    1.091542



** Winsorized Data: 

. reg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w

      Source |       SS           df       MS      Number of obs   =     2,246
-------------+----------------------------------   F(7, 2238)      =      6.43
       Model |  38.1529125         7  5.45041606   Prob > F        =    0.0000
    Residual |  1896.13777     2,238  .847246546   R-squared       =    0.0197
-------------+----------------------------------   Adj R-squared   =    0.0167
       Total |  1934.29068     2,245  .861599413   Root MSE        =    .92046

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |   .7193828   .4026503     1.79   0.074    -.0702243     1.50899
       Capex_w |   .6144666   .1819202     3.38   0.001     .2577167    .9712166
        Size_w |   .0984196   .0268313     3.67   0.000     .0458028    .1510364
         ROE_w |   .0629351   .0245558     2.56   0.010     .0147806    .1110895
      Indebt_w |  -.3134172   .1100432    -2.85   0.004    -.5292147   -.0976198
      Growth_w |  -.0174506   .0493497    -0.35   0.724    -.1142266    .0793254
MdfjonesTACC_w |   .0157689   .0097559     1.62   0.106    -.0033627    .0349006
         _cons |   .7681766   .1671052     4.60   0.000     .4404791    1.095874
--------------------------------------------------------------------------------

** ==> The OLS regression using raw or winsorized data yielded consistent results.

** ==> Winsorization minimally impacts variable means and correlations but improves model robustness by reducing outlier influence, confirming consistent and reliable regression results; thus, winsorized data was used from this point onward.


************************************************************************************************************************************************************************

** 3. Development of Short Panel Data Models

** ==> An initial OLS regression was performed using all observations, ignoring the panel structure, as a baseline reference:

.  regress MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w

      Source |       SS           df       MS      Number of obs   =     2,246
-------------+----------------------------------   F(7, 2238)      =      6.43
       Model |  38.1529125         7  5.45041606   Prob > F        =    0.0000
    Residual |  1896.13777     2,238  .847246546   R-squared       =    0.0197
-------------+----------------------------------   Adj R-squared   =    0.0167
       Total |  1934.29068     2,245  .861599413   Root MSE        =    .92046

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |   .7193828   .4026503     1.79   0.074    -.0702243     1.50899
       Capex_w |   .6144666   .1819202     3.38   0.001     .2577167    .9712166
        Size_w |   .0984196   .0268313     3.67   0.000     .0458028    .1510364
         ROE_w |   .0629351   .0245558     2.56   0.010     .0147806    .1110895
      Indebt_w |  -.3134172   .1100432    -2.85   0.004    -.5292147   -.0976198
      Growth_w |  -.0174506   .0493497    -0.35   0.724    -.1142266    .0793254
MdfjonesTACC_w |   .0157689   .0097559     1.62   0.106    -.0033627    .0349006
         _cons |   .7681766   .1671052     4.60   0.000     .4404791    1.095874
--------------------------------------------------------------------------------

. estimates store ols

** Before conducting regressions, multicollinearity among independent variables was assessed using the Variance Inflation Factor (VIF):

. vif

    Variable |       VIF       1/VIF  
-------------+----------------------
    Indebt_w |      1.15    0.870030
     Capex_w |      1.14    0.874156
      Size_w |      1.11    0.903441
    Growth_w |      1.09    0.915613
MdfjonesTA~w |      1.04    0.959337
        DY_w |      1.03    0.967509
       ROE_w |      1.03    0.972546
-------------+----------------------
    Mean VIF |      1.09

** VIF values close to 1 indicate low multicollinearity; values above 10 would raise concerns. In this case, the mean VIF (~1.09) indicates no multicollinearity issues, supporting the simultaneous inclusion of variables.




************************************************************************************************************************************************************************

** 4. Basic OLS Regression (Short Panel)

. reg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w

      Source |       SS           df       MS      Number of obs   =     2,246
-------------+----------------------------------   F(7, 2238)      =      6.43
       Model |  38.1529125         7  5.45041606   Prob > F        =    0.0000
    Residual |  1896.13777     2,238  .847246546   R-squared       =    0.0197
-------------+----------------------------------   Adj R-squared   =    0.0167
       Total |  1934.29068     2,245  .861599413   Root MSE        =    .92046

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |   .7193828   .4026503     1.79   0.074    -.0702243     1.50899
       Capex_w |   .6144666   .1819202     3.38   0.001     .2577167    .9712166
        Size_w |   .0984196   .0268313     3.67   0.000     .0458028    .1510364
         ROE_w |   .0629351   .0245558     2.56   0.010     .0147806    .1110895
      Indebt_w |  -.3134172   .1100432    -2.85   0.004    -.5292147   -.0976198
      Growth_w |  -.0174506   .0493497    -0.35   0.724    -.1142266    .0793254
MdfjonesTACC_w |   .0157689   .0097559     1.62   0.106    -.0033627    .0349006
         _cons |   .7681766   .1671052     4.60   0.000     .4404791    1.095874
--------------------------------------------------------------------------------


estimates store ols

** ==> Repeated the OLS regression for reference.




************************************************************************************************************************************************************************

** 5. OLS Regression with Clustered Robust Standard Errors


. reg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, vce(cluster Firm_id)

Linear regression                               Number of obs     =      2,246
                                                F(7, 316)         =      10.05
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0197
                                                Root MSE          =     .92046

                                (Std. Err. adjusted for 317 clusters in Firm_id)
--------------------------------------------------------------------------------
               |               Robust
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |   .7193828   .5767119     1.25   0.213    -.4152975    1.854063
       Capex_w |   .6144666   .2076778     2.96   0.003     .2058608    1.023073
        Size_w |   .0984196   .0638374     1.54   0.124    -.0271806    .2240197
         ROE_w |   .0629351   .0525855     1.20   0.232     -.040527    .1663971
      Indebt_w |  -.3134172   .2954421    -1.06   0.290    -.8946995     .267865
      Growth_w |  -.0174506   .0388599    -0.45   0.654    -.0939075    .0590063
MdfjonesTACC_w |   .0157689   .0026411     5.97   0.000     .0105725    .0209653
         _cons |   .7681766    .398386     1.93   0.055    -.0156477    1.552001
--------------------------------------------------------------------------------



estimates store POLS_rob


** To correct for potential heteroskedasticity and autocorrelation within firms, clustered robust standard errors by Firm_id were used.




************************************************************************************************************************************************************************

** 6. Between Effects (BE) Model Estimation

.  reg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, be

      Source |       SS           df       MS      Number of obs   =     2,246
-------------+----------------------------------   F(7, 2238)      =      6.43
       Model |  38.1529125         7  5.45041606   Prob > F        =    0.0000
    Residual |  1896.13777     2,238  .847246546   R-squared       =    0.0197
-------------+----------------------------------   Adj R-squared   =    0.0167
       Total |  1934.29068     2,245  .861599413   Root MSE        =    .92046

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|                     Beta
---------------+----------------------------------------------------------------
          DY_w |   .7193828   .4026503     1.79   0.074                 .0380144
       Capex_w |   .6144666   .1819202     3.38   0.001                 .0756079
        Size_w |   .0984196   .0268313     3.67   0.000                  .080767
         ROE_w |   .0629351   .0245558     2.56   0.010                 .0543911
      Indebt_w |  -.3134172   .1100432    -2.85   0.004                -.0639052
      Growth_w |  -.0174506   .0493497    -0.35   0.724                -.0077342
MdfjonesTACC_w |   .0157689   .0097559     1.62   0.106                 .0345375
         _cons |   .7681766   .1671052     4.60   0.000                        .
--------------------------------------------------------------------------------

. estimates store BE

** ==> The BE model, capturing variation between firms’ averages, was estimated to compare with other panel approaches.




************************************************************************************************************************************************************************

** 7. Fixed Effects (FE) Model Estimation

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, fe

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0422                                         min =          1
     between = 0.0100                                         avg =        7.1
     overall = 0.0085                                         max =         10

                                                F(7,1922)         =      12.11
corr(u_i, Xb)  = -0.3017                        Prob > F          =     0.0000

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.5350251   .2846395    -1.88   0.060     -1.09326    .0232096
       Capex_w |   .1344275   .1252223     1.07   0.283    -.1111583    .3800133
        Size_w |   .4528706   .0646672     7.00   0.000     .3260454    .5796958
         ROE_w |    .001102   .0155767     0.07   0.944    -.0294469     .031651
      Indebt_w |  -.7739904   .1475825    -5.24   0.000    -1.063429   -.4845517
      Growth_w |   .0750195   .0318346     2.36   0.019     .0125855    .1374535
MdfjonesTACC_w |   .0131019   .0062277     2.10   0.036     .0008882    .0253156
         _cons |  -1.218337   .4190228    -2.91   0.004    -2.040124     -.39655
---------------+----------------------------------------------------------------
       sigma_u |  .81900138
       sigma_e |  .52568485
           rho |   .7082227   (fraction of variance due to u_i)
--------------------------------------------------------------------------------
F test that all u_i=0: F(316, 1922) = 15.63                  Prob > F = 0.0000

. estimates store FE

** ==> The FE model was estimated to control for unobserved firm-specific effects.


** 7.1 Also estimated FE with clustered robust standard errors:

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0422                                         min =          1
     between = 0.0100                                         avg =        7.1
     overall = 0.0085                                         max =         10

                                                F(7,316)          =       5.37
corr(u_i, Xb)  = -0.3017                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 317 clusters in Firm_id)
--------------------------------------------------------------------------------
               |               Robust
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.5350251   .2325802    -2.30   0.022    -.9926265   -.0774237
       Capex_w |   .1344275   .1233836     1.09   0.277    -.1083296    .3771846
        Size_w |   .4528706   .1549192     2.92   0.004     .1480672    .7576739
         ROE_w |    .001102   .0121329     0.09   0.928    -.0227695    .0249735
      Indebt_w |  -.7739904   .3436408    -2.25   0.025    -1.450103   -.0978774
      Growth_w |   .0750195   .0350596     2.14   0.033     .0060399    .1439992
MdfjonesTACC_w |   .0131019    .002594     5.05   0.000     .0079981    .0182056
         _cons |  -1.218337   .8945612    -1.36   0.174    -2.978386    .5417116
---------------+----------------------------------------------------------------
       sigma_u |  .81900138
       sigma_e |  .52568485
           rho |   .7082227   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimates store FE_rob



************************************************************************************************************************************************************************

** 8. Random Effects (RE) Model Estimation


. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, re

Random-effects GLS regression                   Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0405                                         min =          1
     between = 0.0105                                         avg =        7.1
     overall = 0.0102                                         max =         10

                                                Wald chi2(7)      =      71.46
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.4167635   .2813169    -1.48   0.138    -.9681344    .1346074
       Capex_w |   .1906109   .1223903     1.56   0.119    -.0492697    .4304914
        Size_w |   .2846959   .0446112     6.38   0.000     .1972596    .3721322
         ROE_w |   .0064148   .0155096     0.41   0.679    -.0239834    .0368131
      Indebt_w |  -.6667527   .1291423    -5.16   0.000     -.919867   -.4136383
      Growth_w |   .0629758   .0315209     2.00   0.046     .0011959    .1247557
MdfjonesTACC_w |   .0121042   .0061822     1.96   0.050    -.0000128    .0242211
         _cons |     -.2192   .2871842    -0.76   0.445    -.7820706    .3436706
---------------+----------------------------------------------------------------
       sigma_u |  .73018341
       sigma_e |  .52568485
           rho |  .65862837   (fraction of variance due to u_i)
--------------------------------------------------------------------------------


. estimates store RE

** ==> The RE model assumes firm-specific effects are random and uncorrelated with regressors.


** 8.1 Also estimated RE with clustered robust standard errors:


. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, re vce(cluster Firm_id)

Random-effects GLS regression                   Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0405                                         min =          1
     between = 0.0105                                         avg =        7.1
     overall = 0.0102                                         max =         10

                                                Wald chi2(7)      =      33.72
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                                (Std. Err. adjusted for 317 clusters in Firm_id)
--------------------------------------------------------------------------------
               |               Robust
          MB_w |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.4167635   .2222175    -1.88   0.061    -.8523017    .0187747
       Capex_w |   .1906109     .11878     1.60   0.109    -.0421936    .4234153
        Size_w |   .2846959   .0813162     3.50   0.000     .1253191    .4440728
         ROE_w |   .0064148   .0122595     0.52   0.601    -.0176133     .030443
      Indebt_w |  -.6667527   .2736585    -2.44   0.015    -1.203113   -.1303919
      Growth_w |   .0629758   .0343786     1.83   0.067     -.004405    .1303566
MdfjonesTACC_w |   .0121042   .0027076     4.47   0.000     .0067973     .017411
         _cons |     -.2192   .4366753    -0.50   0.616    -1.075068    .6366679
---------------+----------------------------------------------------------------
       sigma_u |  .73018341
       sigma_e |  .52568485
           rho |  .65862837   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimates store RE_rob


************************************************************************************************************************************************************************

** 9. Breusch-Pagan Lagrange Multiplier Test for Random Effects

** ==> Tested presence of random effects to decide between RE and OLS.


. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        MB_w[Firm_id,t] = Xb + u[Firm_id] + e[Firm_id,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                    MB_w |   .8615994       .9282238
                       e |   .2763446       .5256848
                       u |   .5331678       .7301834

        Test:   Var(u) = 0
                             chibar2(01) =  3582.34
                          Prob > chibar2 =   0.0000


** Result indicated random effects are preferred.

************************************************************************************************************************************************************************


10. F-Test for Fixed Effects Significance

==> Tested relevance of fixed effects compared to OLS.

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, fe

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0422                                         min =          1
     between = 0.0100                                         avg =        7.1
     overall = 0.0085                                         max =         10

                                                F(7,1922)         =      12.11
corr(u_i, Xb)  = -0.3017                        Prob > F          =     0.0000

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.5350251   .2846395    -1.88   0.060     -1.09326    .0232096
       Capex_w |   .1344275   .1252223     1.07   0.283    -.1111583    .3800133
        Size_w |   .4528706   .0646672     7.00   0.000     .3260454    .5796958
         ROE_w |    .001102   .0155767     0.07   0.944    -.0294469     .031651
      Indebt_w |  -.7739904   .1475825    -5.24   0.000    -1.063429   -.4845517
      Growth_w |   .0750195   .0318346     2.36   0.019     .0125855    .1374535
MdfjonesTACC_w |   .0131019   .0062277     2.10   0.036     .0008882    .0253156
         _cons |  -1.218337   .4190228    -2.91   0.004    -2.040124     -.39655
---------------+----------------------------------------------------------------
       sigma_u |  .81900138
       sigma_e |  .52568485
           rho |   .7082227   (fraction of variance due to u_i)
--------------------------------------------------------------------------------
F test that all u_i=0: F(316, 1922) = 15.63                  Prob > F = 0.0000


** ==> Prob > F = 0.0000 confirms the statistical significance of the fixed effects, supporting the choice of the FE model.




************************************************************************************************************************************************************************

** 11. Hausman Test to Choose Between FE and RE

. hausman FE RE, sigmamore

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       FE           RE         Difference          S.E.
-------------+----------------------------------------------------------------
        DY_w |   -.5350251    -.4167635       -.1182616        .0541168
     Capex_w |    .1344275     .1906109       -.0561834        .0300682
      Size_w |    .4528706     .2846959        .1681747        .0473897
       ROE_w |     .001102     .0064148       -.0053128        .0022857
    Indebt_w |   -.7739904    -.6667527       -.1072377        .0733801
    Growth_w |    .0750195     .0629758        .0120437        .0057431
MdfjonesTA~w |    .0131019     .0121042        .0009977        .0010323
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                  chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       31.63
                Prob>chi2 =      0.0000


**==> P-value < 0.05 rejects null hypothesis, indicating FE is preferred over RE.




************************************************************************************************************************************************************************
** 12. Testing for Heteroskedasticity in FE Model

**==> Used Modified Wald test for groupwise heteroskedasticity.

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, fe

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0422                                         min =          1
     between = 0.0100                                         avg =        7.1
     overall = 0.0085                                         max =         10

                                                F(7,1922)         =      12.11
corr(u_i, Xb)  = -0.3017                        Prob > F          =     0.0000

--------------------------------------------------------------------------------
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.5350251   .2846395    -1.88   0.060     -1.09326    .0232096
       Capex_w |   .1344275   .1252223     1.07   0.283    -.1111583    .3800133
        Size_w |   .4528706   .0646672     7.00   0.000     .3260454    .5796958
         ROE_w |    .001102   .0155767     0.07   0.944    -.0294469     .031651
      Indebt_w |  -.7739904   .1475825    -5.24   0.000    -1.063429   -.4845517
      Growth_w |   .0750195   .0318346     2.36   0.019     .0125855    .1374535
MdfjonesTACC_w |   .0131019   .0062277     2.10   0.036     .0008882    .0253156
         _cons |  -1.218337   .4190228    -2.91   0.004    -2.040124     -.39655
---------------+----------------------------------------------------------------
       sigma_u |  .81900138
       sigma_e |  .52568485
           rho |   .7082227   (fraction of variance due to u_i)
--------------------------------------------------------------------------------
F test that all u_i=0: F(316, 1922) = 15.63                  Prob > F = 0.0000

 
. xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (317)  =  380894630.54
Prob > chi2 =          0.0000

** P-value < 0.05 indicates heteroskedasticity present.




************************************************************************************************************************************************************************

** 13. Fixed Effects Model with Clustered Robust Standard Errors

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.0422                                         min =          1
     between = 0.0100                                         avg =        7.1
     overall = 0.0085                                         max =         10

                                                F(7,316)          =       5.37
corr(u_i, Xb)  = -0.3017                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 317 clusters in Firm_id)
--------------------------------------------------------------------------------
               |               Robust
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |  -.5350251   .2325802    -2.30   0.022    -.9926265   -.0774237
       Capex_w |   .1344275   .1233836     1.09   0.277    -.1083296    .3771846
        Size_w |   .4528706   .1549192     2.92   0.004     .1480672    .7576739
         ROE_w |    .001102   .0121329     0.09   0.928    -.0227695    .0249735
      Indebt_w |  -.7739904   .3436408    -2.25   0.025    -1.450103   -.0978774
      Growth_w |   .0750195   .0350596     2.14   0.033     .0060399    .1439992
MdfjonesTACC_w |   .0131019    .002594     5.05   0.000     .0079981    .0182056
         _cons |  -1.218337   .8945612    -1.36   0.174    -2.978386    .5417116
---------------+----------------------------------------------------------------
       sigma_u |  .81900138
       sigma_e |  .52568485
           rho |   .7082227   (fraction of variance due to u_i)
--------------------------------------------------------------------------------


** ==> The main estimation employs a fixed effects model with robust standard errors clustered by firm (Firm_id), 
correcting for potential heteroskedasticity and within-firm autocorrelation. This approach yields consistent and 
reliable coefficient estimates, improving inference validity.

** ==> The use of clustered robust standard errors effectively corrects heteroskedasticity and autocorrelation in the panel data, providing more reliable inference for the fixed effects estimates.

 


************************************************************************************************************************************************************************
** 14. Additional Robustness Test: Inclusion of Year Fixed Effects

** 14.1 To control for unobserved temporal shocks or macroeconomic effects potentially influencing all firms, we augment the fixed effects model by including year dummies (i.Year). The clustered robust standard errors remain to correct within-firm heteroskedasticity and autocorrelation.

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w i.Year, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.1131                                         min =          1
     between = 0.0045                                         avg =        7.1
     overall = 0.0269                                         max =         10

                                                F(16,316)         =      10.59
corr(u_i, Xb)  = -0.1166                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 317 clusters in Firm_id)
--------------------------------------------------------------------------------
               |               Robust
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |   -.178317   .1828088    -0.98   0.330    -.5379932    .1813592
       Capex_w |   .0972954   .1102471     0.88   0.378    -.1196157    .3142064
        Size_w |   .2278476     .15018     1.52   0.130    -.0676315    .5233267
         ROE_w |   .0085309    .011145     0.77   0.445     -.013397    .0304587
      Indebt_w |  -.7866193   .3345004    -2.35   0.019    -1.444749     -.12849
      Growth_w |   .0705597   .0334039     2.11   0.035     .0048376    .1362818
MdfjonesTACC_w |   .0081351    .003024     2.69   0.008     .0021854    .0140847
               |
          Year |
         2012  |   .0941028   .0312237     3.01   0.003     .0326703    .1555354
         2013  |  -.0074067   .0373229    -0.20   0.843    -.0808394    .0660261
         2014  |  -.1429233   .0423369    -3.38   0.001     -.226221   -.0596256
         2015  |  -.2483066   .0425601    -5.83   0.000    -.3320436   -.1645696
         2016  |   -.174208    .051554    -3.38   0.001    -.2756405   -.0727756
         2017  |   .0218442   .0598193     0.37   0.715    -.0958502    .1395386
         2018  |  -.0485326   .0597366    -0.81   0.417    -.1660643    .0689991
         2019  |   .1461954    .066178     2.21   0.028     .0159901    .2764006
         2020  |   .2497539   .0770659     3.24   0.001     .0981268     .401381
               |
         _cons |   .2453527   .8534678     0.29   0.774    -1.433845     1.92455
---------------+----------------------------------------------------------------
       sigma_u |  .79685295
       sigma_e |  .50706323
           rho |  .71178494   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimates store FE_rob_y

** Year fixed effects capture common time-specific variation that could bias estimates if omitted.



************************************************************************************************************************************************************************
************************************************************************************************************************************************************************


. esttab ols POLS_rob BE RE RE_rob FE FE_rob FE_rob_y using tabela_robustez.txt, b(4) se(4) star(* 0.1 ** 0.05 *** 0.01) stats(N r2 r2_o r2_b r2_w F chi2, fmt(0 3 3 3 3 3 3)) replace
(output written to tabela_robustez.txt)

--------------------------------------------------------------------------------------------------------------------------------------------
                      (1)             (2)             (3)             (4)             (5)             (6)             (7)             (8)   
                     MB_w            MB_w            MB_w            MB_w            MB_w            MB_w            MB_w            MB_w   
--------------------------------------------------------------------------------------------------------------------------------------------
DY_w               0.7194*         0.7194          0.7194*        -0.4168         -0.4168*        -0.5350*        -0.5350**       -0.1783   
                 (0.4027)        (0.5767)        (0.4027)        (0.2813)        (0.2222)        (0.2846)        (0.2326)        (0.1828)   

Capex_w            0.6145***       0.6145***       0.6145***       0.1906          0.1906          0.1344          0.1344          0.0973   
                 (0.1819)        (0.2077)        (0.1819)        (0.1224)        (0.1188)        (0.1252)        (0.1234)        (0.1102)   

Size_w             0.0984***       0.0984          0.0984***       0.2847***       0.2847***       0.4529***       0.4529***       0.2278   
                 (0.0268)        (0.0638)        (0.0268)        (0.0446)        (0.0813)        (0.0647)        (0.1549)        (0.1502)   

ROE_w              0.0629**        0.0629          0.0629**        0.0064          0.0064          0.0011          0.0011          0.0085   
                 (0.0246)        (0.0526)        (0.0246)        (0.0155)        (0.0123)        (0.0156)        (0.0121)        (0.0111)   

Indebt_w          -0.3134***      -0.3134         -0.3134***      -0.6668***      -0.6668**       -0.7740***      -0.7740**       -0.7866** 
                 (0.1100)        (0.2954)        (0.1100)        (0.1291)        (0.2737)        (0.1476)        (0.3436)        (0.3345)   

Growth_w          -0.0175         -0.0175         -0.0175          0.0630**        0.0630*         0.0750**        0.0750**        0.0706** 
                 (0.0493)        (0.0389)        (0.0493)        (0.0315)        (0.0344)        (0.0318)        (0.0351)        (0.0334)   

MdfjonesTA~w       0.0158          0.0158***       0.0158          0.0121*         0.0121***       0.0131**        0.0131***       0.0081***
                 (0.0098)        (0.0026)        (0.0098)        (0.0062)        (0.0027)        (0.0062)        (0.0026)        (0.0030)   

2011.Year                                                                                                                          0.0000   
                                                                                                                                      (.)   

2012.Year                                                                                                                          0.0941***
                                                                                                                                 (0.0312)   

2013.Year                                                                                                                         -0.0074   
                                                                                                                                 (0.0373)   

2014.Year                                                                                                                         -0.1429***
                                                                                                                                 (0.0423)   

2015.Year                                                                                                                         -0.2483***
                                                                                                                                 (0.0426)   

2016.Year                                                                                                                         -0.1742***
                                                                                                                                 (0.0516)   

2017.Year                                                                                                                          0.0218   
                                                                                                                                 (0.0598)   

2018.Year                                                                                                                         -0.0485   
                                                                                                                                 (0.0597)   

2019.Year                                                                                                                          0.1462** 
                                                                                                                                 (0.0662)   

2020.Year                                                                                                                          0.2498***
                                                                                                                                 (0.0771)   

_cons              0.7682***       0.7682*         0.7682***      -0.2192         -0.2192         -1.2183***      -1.2183          0.2454   
                 (0.1671)        (0.3984)        (0.1671)        (0.2872)        (0.4367)        (0.4190)        (0.8946)        (0.8535)   
--------------------------------------------------------------------------------------------------------------------------------------------
N                    2246            2246            2246            2246            2246            2246            2246            2246   
r2                  0.020           0.020           0.020                                           0.042           0.042           0.113   
r2_o                                                                0.010           0.010           0.009           0.009           0.027   
r2_b                                                                0.010           0.010           0.010           0.010           0.004   
r2_w                                                                0.040           0.040           0.042           0.042           0.113   
F                   6.433          10.047           6.433                                          12.110           5.369          10.589   
chi2                                                               71.461          33.725                                                   
--------------------------------------------------------------------------------------------------------------------------------------------
Standard errors in parentheses
* p<0.1, ** p<0.05, *** p<0.01



**==> Summary of Estimation Strategy
** Panel fixed effects model to control for time-invariant unobserved heterogeneity at the firm level.
** Clustered robust standard errors by firm to correct heteroskedasticity and serial correlation.
** Inclusion of year fixed effects as additional control for macroeconomic or industry-wide shocks.
** Models estimated with alternative proxies for accounting information quality based on accruals models.



############################################################################################################################

** 15. Models Using Different Accounting Quality Proxies

** We estimated variants of the baseline model replacing the modified Jones accruals proxy with alternative measures from the literature:




**  15.1 Jones (1991): Mdf_abs_DACC

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w Mdf_abs_DACC i.Year, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,081
Group variable: Firm_id                         Number of groups  =        239

R-sq:                                           Obs per group:
     within  = 0.1008                                         min =          3
     between = 0.0038                                         avg =        8.7
     overall = 0.0298                                         max =         10

                                                F(16,238)         =      11.35
corr(u_i, Xb)  = -0.0301                        Prob > F          =     0.0000

                              (Std. Err. adjusted for 239 clusters in Firm_id)
------------------------------------------------------------------------------
             |               Robust
        MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        DY_w |  -.1494071   .1763039    -0.85   0.398    -.4967224    .1979083
     Capex_w |   .1245459   .1109782     1.12   0.263    -.0940792    .3431709
      Size_w |   .1078682   .1512161     0.71   0.476    -.1900246    .4057611
       ROE_w |   .0122706   .0112247     1.09   0.275    -.0098419    .0343831
    Indebt_w |  -.5288913   .3587366    -1.47   0.142    -1.235596    .1778131
    Growth_w |   .0542907   .0311997     1.74   0.083    -.0071722    .1157536
Mdf_abs_DACC |  -.0002054   .0002718    -0.76   0.450    -.0007408    .0003299
             |
        Year |
       2012  |    .109621    .031625     3.47   0.001     .0473204    .1719215
       2013  |   .0143652   .0372596     0.39   0.700    -.0590356    .0877661
       2014  |  -.1235408   .0419494    -2.94   0.004    -.2061804   -.0409012
       2015  |  -.2333011    .041557    -5.61   0.000    -.3151677   -.1514346
       2016  |  -.1586791    .050944    -3.11   0.002    -.2590378   -.0583204
       2017  |    .045864   .0588046     0.78   0.436    -.0699801     .161708
       2018  |  -.0118731   .0568477    -0.21   0.835     -.123862    .1001157
       2019  |    .219343   .0641052     3.42   0.001      .093057     .345629
       2020  |   .2380507   .0769563     3.09   0.002     .0864482    .3896532
             |
       _cons |   .8856188   .8521957     1.04   0.300     -.793191    2.564429
-------------+----------------------------------------------------------------
     sigma_u |  .83392768
     sigma_e |  .50001316
         rho |  .73556133   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store Mdf_abs_DACC





**  15.2 Modified Jones (Dechow, Sloan & Sweeney, 1995): MdfjonesTACC_w

. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w MdfjonesTACC_w i.Year, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.1131                                         min =          1
     between = 0.0045                                         avg =        7.1
     overall = 0.0269                                         max =         10

                                                F(16,316)         =      10.59
corr(u_i, Xb)  = -0.1166                        Prob > F          =     0.0000

                                (Std. Err. adjusted for 317 clusters in Firm_id)
--------------------------------------------------------------------------------
               |               Robust
          MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
          DY_w |   -.178317   .1828088    -0.98   0.330    -.5379932    .1813592
       Capex_w |   .0972954   .1102471     0.88   0.378    -.1196157    .3142064
        Size_w |   .2278476     .15018     1.52   0.130    -.0676315    .5233267
         ROE_w |   .0085309    .011145     0.77   0.445     -.013397    .0304587
      Indebt_w |  -.7866193   .3345004    -2.35   0.019    -1.444749     -.12849
      Growth_w |   .0705597   .0334039     2.11   0.035     .0048376    .1362818
MdfjonesTACC_w |   .0081351    .003024     2.69   0.008     .0021854    .0140847
               |
          Year |
         2012  |   .0941028   .0312237     3.01   0.003     .0326703    .1555354
         2013  |  -.0074067   .0373229    -0.20   0.843    -.0808394    .0660261
         2014  |  -.1429233   .0423369    -3.38   0.001     -.226221   -.0596256
         2015  |  -.2483066   .0425601    -5.83   0.000    -.3320436   -.1645696
         2016  |   -.174208    .051554    -3.38   0.001    -.2756405   -.0727756
         2017  |   .0218442   .0598193     0.37   0.715    -.0958502    .1395386
         2018  |  -.0485326   .0597366    -0.81   0.417    -.1660643    .0689991
         2019  |   .1461954    .066178     2.21   0.028     .0159901    .2764006
         2020  |   .2497539   .0770659     3.24   0.001     .0981268     .401381
               |
         _cons |   .2453527   .8534678     0.29   0.774    -1.433845     1.92455
---------------+----------------------------------------------------------------
       sigma_u |  .79685295
       sigma_e |  .50706323
           rho |  .71178494   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. 
. estimates store MdfjonesTACC_w




**  15.3 Pae et al. (2005): PAE_abs_DACC


. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w PAE_abs_DACC i.Year, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.1189                                         min =          1
     between = 0.0029                                         avg =        7.1
     overall = 0.0307                                         max =         10

                                                F(16,316)         =      10.14
corr(u_i, Xb)  = -0.0884                        Prob > F          =     0.0000

                              (Std. Err. adjusted for 317 clusters in Firm_id)
------------------------------------------------------------------------------
             |               Robust
        MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        DY_w |  -.1606314    .179755    -0.89   0.372    -.5142992    .1930364
     Capex_w |   .0509638   .1050155     0.49   0.628    -.1556542    .2575817
      Size_w |   .1914648   .1448892     1.32   0.187    -.0936046    .4765342
       ROE_w |   .0122259   .0109789     1.11   0.266     -.009375    .0338268
    Indebt_w |  -.7512556   .3311171    -2.27   0.024    -1.402728   -.0997829
    Growth_w |   .0556373     .03072     1.81   0.071    -.0048044     .116079
PAE_abs_DACC |   .3007877   .1475912     2.04   0.042      .010402    .5911734
             |
        Year |
       2012  |   .0999687   .0314899     3.17   0.002     .0380123    .1619252
       2013  |  -.0055553   .0372204    -0.15   0.881    -.0787866    .0676759
       2014  |  -.1328917   .0430107    -3.09   0.002    -.2175153   -.0482682
       2015  |  -.2415289   .0426137    -5.67   0.000    -.3253714   -.1576864
       2016  |  -.1969056    .050256    -3.92   0.000    -.2957844   -.0980268
       2017  |   .0315102   .0605616     0.52   0.603    -.0876447     .150665
       2018  |  -.0388848   .0600594    -0.65   0.518    -.1570516     .079282
       2019  |   .1679146   .0665717     2.52   0.012     .0369348    .2988944
       2020  |   .1989001     .07586     2.62   0.009     .0496457    .3481546
             |
       _cons |   .4321182    .826209     0.52   0.601    -1.193448    2.057684
-------------+----------------------------------------------------------------
     sigma_u |  .79640438
     sigma_e |  .50538618
         rho |  .71291184   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. estimates store PAE_abs_DACC





**  15.4 Francis et al. (2005): ROA_abs_DACC


. xtreg MB_w DY_w Capex_w Size_w ROE_w Indebt_w Growth_w ROA_abs_DACC i.Year, fe vce(cluster Firm_id)

Fixed-effects (within) regression               Number of obs     =      2,246
Group variable: Firm_id                         Number of groups  =        317

R-sq:                                           Obs per group:
     within  = 0.1206                                         min =          1
     between = 0.0032                                         avg =        7.1
     overall = 0.0332                                         max =         10

                                                F(16,316)         =      10.25
corr(u_i, Xb)  = -0.0771                        Prob > F          =     0.0000

                              (Std. Err. adjusted for 317 clusters in Firm_id)
------------------------------------------------------------------------------
             |               Robust
        MB_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        DY_w |  -.1605595   .1782446    -0.90   0.368    -.5112557    .1901367
     Capex_w |   .0464317    .106339     0.44   0.663    -.1627901    .2556535
      Size_w |   .1806823   .1424581     1.27   0.206    -.0996039    .4609686
       ROE_w |   .0103667   .0109454     0.95   0.344    -.0111683    .0319017
    Indebt_w |  -.7411208   .3310364    -2.24   0.026    -1.392435   -.0898069
    Growth_w |    .053149   .0295065     1.80   0.073     -.004905     .111203
ROA_abs_DACC |   .3276281   .1803703     1.82   0.070    -.0272505    .6825066
             |
        Year |
       2012  |     .09951    .031535     3.16   0.002     .0374649    .1615551
       2013  |  -.0068545   .0370847    -0.18   0.853    -.0798186    .0661097
       2014  |  -.1341446   .0430465    -3.12   0.002    -.2188384   -.0494507
       2015  |  -.2383307   .0434388    -5.49   0.000    -.3237965   -.1528649
       2016  |  -.1707915    .052209    -3.27   0.001    -.2735128   -.0680703
       2017  |   .0330105   .0609612     0.54   0.589    -.0869307    .1529516
       2018  |  -.0365454   .0600618    -0.61   0.543     -.154717    .0816262
       2019  |   .1709547   .0667633     2.56   0.011     .0395979    .3023115
       2020  |   .1743186    .080188     2.17   0.030     .0165487    .3320885
             |
       _cons |   .4976765   .8093375     0.61   0.539    -1.094695    2.090048
-------------+----------------------------------------------------------------
     sigma_u |  .79535893
     sigma_e |  .50490334
         rho |  .71276539   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. estimates store ROA_abs_DACC




** ==> Each model includes the same control variables and year fixed effects, with standard errors clustered by firm.

. esttab Mdf_abs_DACC MdfjonesTACC_w PAE_abs_DACC ROA_abs_DACC using tabela_modelos_qualidade.txt, b(4) se(4) star(* 0.1 ** 0.05 *** 0.01) stats(N r2 r2_o r2_b r2_w F, fmt(0 3 3 3 3 3)) replace



----------------------------------------------------------------------------
                      (1)             (2)             (3)             (4)   
                     MB_w            MB_w            MB_w            MB_w   
----------------------------------------------------------------------------
DY_w              -0.1494         -0.1783         -0.1606         -0.1606   
                 (0.1763)        (0.1828)        (0.1798)        (0.1782)   

Capex_w            0.1245          0.0973          0.0510          0.0464   
                 (0.1110)        (0.1102)        (0.1050)        (0.1063)   

Size_w             0.1079          0.2278          0.1915          0.1807   
                 (0.1512)        (0.1502)        (0.1449)        (0.1425)   

ROE_w              0.0123          0.0085          0.0122          0.0104   
                 (0.0112)        (0.0111)        (0.0110)        (0.0109)   

Indebt_w          -0.5289         -0.7866**       -0.7513**       -0.7411** 
                 (0.3587)        (0.3345)        (0.3311)        (0.3310)   

Growth_w           0.0543*         0.0706**        0.0556*         0.0531*  
                 (0.0312)        (0.0334)        (0.0307)        (0.0295)   

Mdf_abs_DACC      -0.0002                                                   
                 (0.0003)       

MdfjonesTA~w                       0.0081***                                
                                 (0.0030)                                   

PAE_abs_DACC                                       0.3008**                 
                                                 (0.1476)                   

ROA_abs_DACC                                                       0.3276*  
                                                                 (0.1804)   

2011.Year          0.0000          0.0000          0.0000          0.0000   
                      (.)             (.)             (.)             (.)   

2012.Year          0.1096***       0.0941***       0.1000***       0.0995***
                 (0.0316)        (0.0312)        (0.0315)        (0.0315)   

2013.Year          0.0144         -0.0074         -0.0056         -0.0069   
                 (0.0373)        (0.0373)        (0.0372)        (0.0371)   

2014.Year         -0.1235***      -0.1429***      -0.1329***      -0.1341***
                 (0.0419)        (0.0423)        (0.0430)        (0.0430)   

2015.Year         -0.2333***      -0.2483***      -0.2415***      -0.2383***
                 (0.0416)        (0.0426)        (0.0426)        (0.0434)   

2016.Year         -0.1587***      -0.1742***      -0.1969***      -0.1708***
                 (0.0509)        (0.0516)        (0.0503)        (0.0522)   

2017.Year          0.0459          0.0218          0.0315          0.0330   
                 (0.0588)        (0.0598)        (0.0606)        (0.0610)   

2018.Year         -0.0119         -0.0485         -0.0389         -0.0365   
                 (0.0568)        (0.0597)        (0.0601)        (0.0601)   

2019.Year          0.2193***       0.1462**        0.1679**        0.1710** 
                 (0.0641)        (0.0662)        (0.0666)        (0.0668)   

2020.Year          0.2381***       0.2498***       0.1989***       0.1743** 
                 (0.0770)        (0.0771)        (0.0759)        (0.0802)   

_cons              0.8856          0.2454          0.4321          0.4977   
                 (0.8522)        (0.8535)        (0.8262)        (0.8093)   
----------------------------------------------------------------------------
N                    2081            2246            2246            2246   
r2                  0.101           0.113           0.119           0.121   
r2_o                0.030           0.027           0.031           0.033   
r2_b                0.004           0.004           0.003           0.003   
r2_w                0.101           0.113           0.119           0.121   
F                  11.354          10.589          10.138          10.245   
----------------------------------------------------------------------------
Standard errors in parentheses
* p<0.1, ** p<0.05, *** p<0.01

** We present comparative results of these models in tabular form, showing coefficient estimates, robust standard errors, and significance levels. The consistency of the key variables' effects across models reinforces the robustness of the findings.


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